Wikipedia:Reference desk/Archives/Science/2013 May 22

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May 22

More questions about earth-moon distance

Hi again. A yesterday I asked "Hi: I looked up the entry for the Moon, trying to read what was the original distance between the Earth and Moon. I did not see it in the story. Did I miss it or is it not there? Thanks for you help. Red.leaf.flyers (talk) 16:53, 20 May 2013 (UTC)". Since then I realized I should clarify my question. I regularly listen to a CBC radio science program called "Quirks and Quarks". I was asking my original question based on an episode I heard some years ago, where a scientist in some astro field said that the moon was previously about half as far from Earth as it is now. Apparently there are grounds to think that some substantial impact pushed the moon out much further. I wish I could remember more of that interview. Thanks for all the responses to my original question. Cool stuff! Red.leaf.flyers (talk) 02:06, 22 May 2013 (UTC)

The giant impact hypothesis seems to be by far the most popular one now, given the modelling. The Moon would have been quite closer in than half the current distance. There is no evidence I am aware of of a second impact that would have pushed the Moon out further after that. Analyses of the Moon's composition provide no evidence of that, and its current orbit is entirely compatible with the "Persephone" model; at least there is no contradiction of this in the popular press for the last decade. For other theories see origin of the moon. μηδείς (talk) 03:12, 22 May 2013 (UTC)

Which types of dogs lives longer, larger dogs or smaller dogs?

The Chinese article says smaller dogs lives longer. Are there any differences?--朝鲜的轮子 (talk) 03:18, 22 May 2013 (UTC)

Large dogs are notoriously short-lived, with Irish Wolfhounds and Great Danes living 6 to 8, and sometimes 10 years, as noted in those articles. Generally, the smaller the dog, the longer the lifespan. Acroterion (talk) 03:21, 22 May 2013 (UTC)

Here's a good source backing up small dogs living longer: Which dogs live longest? Red Act (talk) 03:41, 22 May 2013 (UTC)

(EC)I just found the same article:) this article is interesting. It says that it's the weight that matters not necessarily the height and that generally dogs under 30 lbs live the longest. Vespine (talk) 03:45, 22 May 2013 (UTC)

Measuring entropy

How can one actually measure the total entropy of a system? 130.56.235.221 (talk) 05:04, 22 May 2013 (UTC)

Entropy is often defined thermodynamically; you don't measure it directly, you derive it from other measurements of the system. A fairly easy way to define it would be from the Gibbs free energy equation: the entropy of a system is simply S = (H-G)/T; that is you subtract the free energy from the enthalpy and divide that result by the temperature. In practical terms, you don't measure any of these values directly, you measure them as incremental changes as, for example, a chemical reaction progresses. So, we generally say then that ΔS =(ΔH-ΔG)/T, where the Δ values are the changes in those values you get as a result of changes to the system; so for a chemical reaction you can get ΔH by calorimetry, knowing that for a constant pressure system, ΔH is equal to the heat evolved or absorbed during the chemical reaction. ΔG can be calculated from the equilibrium constant, ΔG = -RT ln (K) which itself is calculated from the relative concentrations of the substances involved in the reaction. T is measured directly. So, you can calculate ΔS by going through several sets of calculations based on measurements you can make from first principles (i.e. concentrations, temperatures, etc.) --Jayron32 05:35, 22 May 2013 (UTC)

Special Relativity: follow up

In order for Special Relativity to develop its equations (e.g. Lorentz transformations), it's essential to assume that the speed of light does not depent on the inertial system measuring that speed; Is it essential to assume that the speed of light does not change over time/space either? HOOTmag (talk) 19:21, 12 May 2013 (UTC)

It's not essential to start from the constancy of the speed of light. Einstein did it that way in 1905 because at that time everyone knew that the speed of light was c but couldn't figure out what that speed was relative to, and he wanted to point out that you can just take the speed to be c, full stop, not relative to anything in particular, without any logical contradiction. There are other ways of motivating special relativity, though. For example, you can derive it from the reciprocity of redshifts: if two rocket ships move inertially away from a common starting point, each one sees the other redshifted by the same factor. That gets you a theory with the same mathematical structure as Einstein's theory that doesn't say anything about the speed of light as such. You can then, in the course of defining your system of units, take the speed of light to be constant. You don't have to, but you can without any contradiction—that's what distinguishes special relativity from Newtonian physics.

So it doesn't really make sense to ask whether the speed of light varies with position or time since that depends on how you define your units of measurement. A real time variation of physical constants would show up as a change in some other measurable quantity, such as the electron-proton mass ratio. -- BenRG 21:02, 12 May 2013 (UTC)

Admittedly, I'm rather surprised by your response. As far as I understand, Lorentz transformations are results of Special relativity, aren't they? Whereas assuming them is mathematically equivalent to assuming that the speed of light does not depend on the inertial system measuring that speed, isn't it? Hence, assuming that the speed of light does depend on the inertial system, contradicts Special Relativity, doesn't it? I'm just asking whether assuming that the speed of light changes over time - contradicts Special Relativity. HOOTmag (talk) 21:20, 12 May 2013 (UTC)

On the first point, it would be more correct to say that special relativity is a result (or an application) of the Lorentz transformation, rather than the other way round - see History of Lorentz transformations. Tevildo (talk) 23:24, 12 May 2013 (UTC)

From a historical retrospective point of view - you're right, but I'm talking from a relativistic point of view. Einstein concluded Lorentz transformations from the constancy of speed of light, not vice versa. HOOTmag (talk) 07:20, 13 May 2013 (UTC)

Minkowski spacetime is homogeneous in space and time, and you need some assumption to distinguish that from some other spacetime geometry that isn't, but I'm not sure that gets at the core of your question. The meaning of "speed" in Einstein's postulate is not obvious a priori, since the paper argued that the seemingly obvious notions of distance and time that physicists had had until then were actually wrong. Einstein uses the postulate to justify his method of synchronizing clocks, and it's not until the synchronized clocks are introduced that the inertial reference frames are defined and the "speed" in the original postulate has a clear meaning. That's okay because all physical theories are circular in that way (see this thread, the final reply beginning "There is an unavoidable circularity...", where I think I explained this better than I'm doing it here). The postulates in the original paper are a jumping-off point for the argument, but because of the circularity they aren't really postulates in a formal mathematical sense, and there's no useful distinction to be made between assumptions and conclusions. -- BenRG 07:33, 13 May 2013 (UTC)

Logically speaking - every assumption is a conclusion, while for the practical purpose of the current thread - I don't distinguish between assumptions and conclusions. By saying that A is an assumption/conclusion of B, I just mean that the negation of A contradicts B. As for Minkowski spacetime: My original question refers to Minkowski's relativistic equations as well. HOOTmag (talk) 08:23, 13 May 2013 (UTC)

I think the word for which you're looking is consequence. Conclusions are whatever propositions that are designated as conclusions (i.e, meant to be proved). If an assumption is not designated as a conclusion (and they usually aren't), then it isn't one. --Atethnekos (Discussion, Contributions) 17:23, 13 May 2013 (UTC)

As explained here, the speed of light is not a real physical constant. Count Iblis (talk) 23:51, 12 May 2013 (UTC)

Other users are giving IMO unnecessarily complicated answers, so to keep it simple the answer to OP's question is yes. In his 1905 paper, Einstein mentions explicitly (albeit briefly) that "it is clear that the [Lorentz transformations] must be linear on account of the properties of homogeneity which we attribute to space and time", which basically implies that the speed of light doesn't change in space or time. 65.92.6.9 (talk) 03:01, 13 May 2013 (UTC)

And, by "homogeneity," Einstein means to say that the value of the permittivity of free space and the permeability of free space - commonly, ε₀ and μ₀ - are well-defined and always constant at all positions. From this postulate, the equation of retarded time is trivially found by solving Maxwell's equations. The Lorentz transform is a mere algebraic simplification of the more general form.

By coincidence, I had been reading The Sign of the Four this evening - published 1890 - and it referenced (very indirectly) the Elements of the Philosophy of Newton by Voltaire (Holmes is quoting a pithy bit of French, and alluding to shedding some light on the case). Naturally, my inclination was to track down the text, and read as much of it as I could... it is available online (but not at Project Gutenberg, unfortunately, nor in English translation - here it is at Elementi della filosofia di Newton). It is absolutely amazing! To read Voltaire succinctly express Isaac Newton's optics - to talk about the constancy of the speed of light, and to talk of light as both a ray and as a particle... published in the year 1738 as a regurgitation of Newton's earlier and far more technical writings on optics - a thought crossed my mind, which I will summarize here... "those who think Einstein's work was really amazing have not spent enough time reading the works of his predecessors." Nimur (talk) 04:04, 13 May 2013 (UTC)

See Standing on the shoulders of giants, a quote not created by, but often attributed to, Newton on his own work. It applies to every scientist in history since the first caveman tried to make fire. --Jayron32 04:28, 13 May 2013 (UTC)

The giants on whose shoulders the cavemen stood were, of course, the nephilim. I'm not exactly sure how standing on a nephil's shoulder helps you make fire, but there you are. --Trovatore (talk) 08:11, 17 May 2013 (UTC)

OP's comment: I still wonder which relativistic equation must result in the constancy of speed of light in space/time. The equation of retarded time - just results in the equation: $c={\frac {|\mathbf {r} -\mathbf {r} '|}{t-t_{r}}}$, which does not tell us whether the very value: ${\frac {|\mathbf {r} -\mathbf {r} '|}{t-t_{r}}}$ is constant. Note that Lorentz transformations do tell us that the speed of light does not depend on the inertial system measuring that speed. HOOTmag (talk) 07:20, 13 May 2013 (UTC)

You are confusing a result with a derivation. The derivation proceeds along a line of mathematical reasoning that starts by solving Maxwell's equations for a moving source. This gives a description of the electric and magnetic fields at all points in space and time. From that, a lot of algebraic manipulation gives you a wave equation with a propagation speed, independent of the motion of the source. Our articles cover these topics, but this is fairly advanced mathematics and physics. My recommendation is to begin studying the wave equation in its classical form, until it is so intimately familiar to you that you recognize it, even when obfuscated by multiple independent variables. Then you will be able to identify propagation velocity by inspection. More bluntly: even if you are an autodidact, you require a many years of mathematical preparation before you can reasonably interpret and use the equations that govern the relativistic behavior of light. Commonly, this means three to five years of rigorous study of introductory calculus and physics at a university level. It's a bit unreasonable to think that an encyclopedia can expedite that process to just a few days or hours. Nimur (talk) 14:56, 13 May 2013 (UTC)

No, I was not confusing a result with a derivation: I just wondered "which relativistic equation must result [by a mathematical derivation] in the constancy of speed of light in space/time". Anyways, as opposed to what you've claimed, I don't think one needs "three to five years of rigorous study of introductory calculus and physics at a university level" in order to answer my original question. HOOTmag (talk) 08:22, 16 May 2013 (UTC)

I said that mathematical preparation is usually necessary. You might be a genius beyond everyone's wildest expectations. But you're still asking the same question, which has already been answered incredibly thoroughly, leading me to believe that you don't have the prerequisite context so that you can understand the answer. Which part are you still stumbling on? A constant speed of light is a direct consequence of the assumption that the permittivity of free space and the permeability of free space - commonly, ε₀ and μ₀ - are well-defined and always constant at all positions. These parameters define the speed of light in our best theories of electromagnetics, and this premise matches physical experiment. Are you unable to see the link between physical observation and the equation that models it? If so, I suggest you start reading about electrostatics, and then electrodynamics. Nimur (talk) 13:58, 16 May 2013 (UTC)

The well-known constants ε₀ and μ₀ are really assumed to be constant at all positions, and we undoubtedly shouldn't forget that Einstein was highly inspired by their constancy when he developed his relativistic mechanics, even without us mentioning the important role played in electromagnetism by Special Relativity (e.g. by its motivating the "manifestly covariant" tensor form, and by giving formulas for how the electric and magnetic fields are altered under a Lorentz transformation from one inertial frame of reference to another, and by showing that the frame of reference determines whether the observation follows electrostatic or magnetic laws). However, I was not asking about relativistic electromagnetism, nor about the psychological inspiration of the constants ε₀ and μ₀ in Einstein's mind when he developed his relativistic mechanics. I was just interested in relativistic mechanics per se, i.e. in its explicit assumptions (e.g. the constancy of speed of light) and in its results (e.g. Lorentz transforms). Relativistic mechanics involves concepts like: time, space, mass, force, momentum, energy and the like, yet not concepts like electric charge or magnetic field. Relativistic mechanics assumes/concludes some claims, e.g. the equation of time dilation (and likewise), yet not any claim about ε₀ and μ₀, so that one can study relativistic mechanics, without having studied Maxwell's theory, and still wonder whether - one must assume/conclude the constancy of speed of light in time/space - in order to fully grasp the fundamental principles of relativistic mechanics.

As for mathematics: as a mathematician I can assure you that one needs no advanced mathematics for understanding whether the constancy of speed of light in time/space is needed for relativistic mechanics. HOOTmag (talk) 17:51, 16 May 2013 (UTC)

ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2. It's really not different from the factors of 1 multiplying dx^2, dy^2 and dz^2, which you can relate to Pythagoras' theorem (and which you can change to arbitrary values by using different units for measuring distances in the x, y and z directions). Count Iblis (talk) 13:12, 13 May 2013 (UTC)

The invariant ds^2 = dx^2 + dy^2 + dz^2 - c^2 dt^2, only shows that c can't depend on the inertial frame. However, this invariant may vary in time, hence - one can suppose c itself varies in time - without contradicting the very invariant mentioned above. HOOTmag (talk) 08:22, 16 May 2013 (UTC)

Yes, but the c in this equation doesn't have any physical meaning whatsoever, you can just set it equal to 1. It's similar to writing the first law of thermodynamics as dE = dQ - p dW instead of dE = dQ - dW, because we could insist on using different units for measuring work and heat; we could have assigned work a different dimension from heat making the units for work incompatible with the unit for heat. You could then ask if you could prove using the laws of thermodynamics that p is a constant, if it can depend on time etc. etc.

Just like E = m c^2 says that mass is equivalent to energy in the sense that a box containing an amount of mass m in rest will have a total energy content of m c^2, we would say that an amount of work dW done by a system results in removing an amount of energy of p dW from the system. Advanced books on thermodynamics would work in p = 1 units. But at high school level, teachers would insist that work is not energy, as they have different units. Count Iblis (talk) 14:01, 17 May 2013 (UTC)

No, you can't "just set it equal to 1", because it may equal to 1 meter per second - today, but may equal 2 meters per second - tomorrow. Let's take your simple example of E = m c^2, whereby m is measured in units of mass (e.g. kg), c in units of velocity (e.g. meter / second) and E in units of mass X velocity X velocity (e.g. as above). Please notice that this equation is still consistent with the assumption that c varies in time, so that c may equal 1 meter per second - today, and will equal 2 meters per second - tomorrow. HOOTmag (talk) 16:03, 17 May 2013 (UTC)

But then you should first remove all the extraneous non-physcal degrees of freedom to make sure that any change is indeed a change in the physics. Units are by definition such non-physical degrees of freedom which should be removed in these sort of discussions. What you should do instead is consider the equations of special relativity in natural units and then make these time dependent. Otherwise, what you are doing now is equivalent to actually taking these equations in natural units, insert c considered as a scaling constant in various places see here for details and then saying that this c could be time dependent which then by construction won't affect the physics. Count Iblis (talk) 16:37, 17 May 2013 (UTC)

Let's take Newton's equation: E_k=mv²/2. The units of E are defined to be: mass X velocity X velocity, and nobody claims that we can set v equal to 1. Newton didn't have to use any constant , say p, for making the link between the E_k and the mv²/2, because if he had used such a constant, say p, then we could set p equal to 1!

250 years later, Einstein replaced Newton's equation by the equation: E_k=(m-m₀)c²; Please notice that m₀ is an invariant (i.e. does not depend on the frame of reference), but may still vary in time (e.g. when an electron and a positron collide)! So why can't c (whose unit is velocity) be an invariant which varies in time - just like m₀, while the constant p - which could be supposed to make the link between the E_k and the (m-m₀)c² - is set to 1!

To sum up, my question is very simple: if we assumed that the units of E are still (as in Newton's theory): mass X velocity X velocity, and that the invariant c varies in time/space - just as m₀ varies in time - and just as v (in Newton's equation mentioned above) varies in time, would that contradict any of the (well known) relativistic equations, e.g. Lorentz transforms, or the Minkowski invariants (and the like)? HOOTmag (talk) 19:18, 18 May 2013 (UTC)

If c(x,t) is such that the Riemann curvature tensor is zero, then you get the usual relativistic equations after a suitable coordinate transform. Count Iblis (talk) 22:59, 18 May 2013 (UTC)

You could get the usual relativistic equations - even if c(x,t) could depend on (x,t). HOOTmag (talk) 23:49, 18 May 2013 (UTC)

Introducing a c(x,t) doesn't make c(x,t) the speed of light that you would measure. I think you fail to understand that the units can't be fixed in the way you are assuming, because they are always unphysical gauge degrees of freedom. A simple example would be to consider the Schwarzschild metric. It has an effective c(r) in there, but the speed of light is simply constant and the physics is not the same as what is in a flat space-time. Count Iblis (talk) 13:12, 19 May 2013 (UTC)

I do understand that the units are always unphysical gauge degrees of freedom. However, I have already explained - in my response preceding my previous response - why all of this stuff has nothing to do with my original question. So let me remind you what my original question has been about:

1. As I have already shown in this thread (on 17 May at 16:03), it's mathematically provable - from some (well known) equations of Relativistic mechanics - that c does not depend on the frame of reference, i.e. that every pair of velocities v,v' satisfies c(v)=c(0)=c(v'). So I've only been asking, whether it's also mathematically provable - from any set of (well known) equations of Relativistic mechanics - that c does not depend on time either, i.e. that every pair of moments t,t' satisfies c(t)=c(0)=c(t').

2. All of experimental information we have accumulated - really approves of the assumption that c does not depend on time, i.e. that every pair of moments t,t' satisfies c(t)=c(t'). So I've only been asking whether this experimental fact can also be mathematically inferred from any set of (well known) equations of Relativistic mechanics, just as we can mathematically infer a parallel conclusion about the invariance of c with respect to frames of reference. HOOTmag (talk) 18:33, 19 May 2013 (UTC)

To address the OP's original question, if you require that a Lorentz boost has the same mathematical structure that it does now, and that boosts be invertible such that a boost by velocity ${\vec {v}}$ followed by a boost by velocity $-{\vec {v}}$ should return the original coordinate system then it follows that the speed of light field must be a Lorentz invariant, i.e. $c(x,y,z,t)=c(x',y',z',t')$ measures the same value for all possible Lorentz transforms. This generally implies that the speed of light is a constant independent of space and time. Now, one could replace a Lorentz boost by an integral composition of differential boosts in such a way that one could self-consistently describe a world where the measured value of the speed of light varied in space and time; however, the math then describing a change of inertial reference frame would be more complicated then the current Lorentz transformation. Dragons flight (talk) 19:44, 13 May 2013 (UTC)

On reflection, one can also have a solution where only allows the speed of light field to transform with the boost. That version is also fairly natural, but would require forgoing the idea that all observers can agree on the way the speed of light changes in space and time. Dragons flight (talk) 23:18, 13 May 2013 (UTC)

I still wonder about how you derive that $c(x,y,z,t)=c(x',y',z',t')$ in the same inertial frame. HOOTmag (talk) 09:31, 16 May 2013 (UTC)

That's a trivial consequence of spacetime homogeneity. Dauto (talk) 14:18, 17 May 2013 (UTC)

You haven't showed directly (rigorously) how the constancy of speed of light in spacetime is a consequence of spacetime homogeneity, although the constancy of my velocity is not a consequence of spacetime homogeneity.

Just to let you figure out what I mean by direct rigorous proof, I will prove you now - directly-rigorously - why the relativistic equation of time dilation alone, must assume - and must result in - the constancy of speed of light in all inertial frames, i.e. I will prove directly and rigorously that - assuming the speed of light depends on the inertial frame - contradicts the relativistic equation of time dilation, and the proof for that is quite simple:

Special Relativity results in the equation of time dilation: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c^{2}}}}$. If $c$ had depended on the inertial frame, then that equation would have meant: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ , so we would have received:

(1) ${\frac {\Delta t_{v}{\sqrt {c_{v}^{2}-v^{2}}}}{\Delta t_{0}}}=c_{v}$.

However, if we hadn't used the equation of time dilation nor Lorentz transforms nor Special Relativity, but rather had used pure mathematics only, then we would have concluded that: $c_{0}\Delta t_{0}=\Delta L={\sqrt {c_{v}^{2}-v^{2}}}\Delta t_{v}$ , so we would have received:

(2) ${\frac {\Delta t_{v}{\sqrt {c_{v}^{2}-v^{2}}}}{\Delta t_{0}}}=c_{0}$.

Combining (1) with (2) gives: $c_{v}=c_{0}$ , i.e. $c$ does not depend on the inertial frame.

HOOTmag (talk) 16:03, 17 May 2013 (UTC)

Your math formulation is wrong. Consider these two diagrams. Let the case where the two panels appear at rest be denoted case 0, and the case where they are moving as case v. In the first case, light travels:

$2L=c_{0}\Delta t_{0}$

In the second case, it travels:

$2D=c_{v}\Delta t_{v}=2{\sqrt {\left({\frac {1}{2}}v\Delta t_{v}\right)^{2}+L^{2}}}$

Giving:

$\Delta t_{v}={\frac {\frac {2L}{c_{v}}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$

Which ultimately implies:

$\Delta t_{v}={\frac {c_{0}}{c_{v}}}{\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$

That's the correct relativistic description of time dilation if you want to assume that c depends on the frame of reference. By not including the prefactor, you implicitly assumed that $c_{0}=c_{v}$, which makes your proof circular. Dragons flight (talk) 09:51, 19 May 2013 (UTC)

No, I didn't assume that $c_{0}=c_{v}$, but your diagram is not mine, so both your calculation and my calculation are correct, since each one refers to a different diagram! Your diagram involves two (right) triangles, whereas my diagram involves one (right) triangle only. Additionally, your calculation uses the Pythagorean theorem for calculating the length of path, whereas my calculation uses the Pythagorean theorem for calculating the length of velocity. Anyways, both my diagram and my calculation are simpler than yours. If you follow them according to my current explanation, you'll realize that my calculation does not assume that $c_{0}=c_{v}$ and is definitely correct. HOOTmag (talk) 21:36, 19 May 2013 (UTC)

As I said, the proof is trivial. It requires no math. By definition, spacetime homogeneity means that all properties of spacetime are homogeneous. In other words, all parameters necessary to describe the vacuum are constant - they cannot depend on the coordinates of specific place where you're chose to do your experiments. The constant "c" (known by the misnomer "speed of light") is one such parameter and therefore cannot depend on the coordinates. Dauto (talk) 17:31, 17 May 2013 (UTC)

Why is it a misnomer? -- Jack of Oz ^[Talk] 20:31, 17 May 2013 (UTC)

c is a constant related to the geometry of space-time. Photons have a mass of zero and travel at the speed of c. But to say that c is the speed of light is similar to saying that the number 0 is the mass of light :) Count Iblis (talk) 20:40, 17 May 2013 (UTC)

So, what in fact is the speed of light (commonly denoted c), if not what we say in our article speed of light? -- Jack of Oz ^[Talk] 20:58, 17 May 2013 (UTC)

Did you read the article? The first paragraph makes it clear that c is a physical constant and light - as all massless objects - travels at that speed. We might just as well call it "speed of gravity", or "square-root-of-mass-energy-conversion-factor", but the best choice would be "spacetime conversion factor" because that's what c is: a factor that allows us to convert between two units. To say that c = 299,792,458 m/s is equivalent to say that the conversion factor between inches and millimeters is 25.4 mm/inches. Dauto (talk) 23:32, 17 May 2013 (UTC)

Not the entire article, but enough. It seems to be saying that the name of the physical constant is "the speed of light" (from which the article derives its title), and its symbol is "c" (this would certainly square with how people call c "the speed of light"). Are you saying that it should be saying something different? If so, what? -- Jack of Oz ^[Talk] 01:17, 18 May 2013 (UTC)

No it should not be saying something different. Speed of light is the universally accepted name for the constant. the point is that if you want to really understand the meaning of that constant than you should try to avoid seeing it simply as a description of how fast light moves. It has a much deeper meaning than that. As Count Iblis pointed out, c plays a very important role in the understanding of the nature of spacetime itself. Dauto (talk) 02:59, 18 May 2013 (UTC)

Thanks. I certainly understand that it's not just light, but all EM radiation etc that travels at c. However, if you can say that "Speed of light is the universally accepted name for the constant", then how can you argue that that very expression is a misnomer? What would you prefer we all call it? -- Jack of Oz ^[Talk] 03:15, 18 May 2013 (UTC)

It is a misnomer because being the speed of light is not the only fact (or even the most important fact) about that constant. As Count Iblis said, nobody thinks of the number zero as "the mass of light", why should we think of c as the speed of light. Nevertheless, "speed of light" IS the universally accepted term and that's what we all should call it. Misnomer or not, that's its name. Dauto (talk) 15:40, 18 May 2013 (UTC)

No argument here. I was just looking for any substance to your original point, and we now agree there wasn't any. Thanks for clearing that up. -- Jack of Oz ^[Talk] 22:47, 18 May 2013 (UTC)

There is a point. You just missed it. Sorry I couldn't help you. Dauto (talk) 17:53, 22 May 2013 (UTC)

@Dauto, you assume what was to be demonstrated. I'm asking: does any (well known) relativistic equation (e.g. Lorentz transforms, or the Minkowski invariants) need to assume that the invariant c is (as you put it): "one of such parameters necessary to describe the vacuum"? In other words, if we assumed that the invariant c is not "one of such parameters necessary to describe the vacuum", but rather varies in time/space, would that contradict any of the (well known) relativistic equations, e.g. Lorentz transforms, or the Minkowski invariants (and the like)? This is my question! HOOTmag (talk) 18:20, 18 May 2013 (UTC)

Yes, a varying c would mess up the invariants. For instance, the invariant mass $m^{2}c^{4}=(E^{2}+c^{2}p^{2})$ would change overtime unless either the energy or the momentum of the particle isn't conserved. Dauto (talk) 20:07, 18 May 2013 (UTC)

But the invariant mass (i.e. the "rest mass") does change over time (e.g. when an electron and a positron collide)! Einstein has never claimed that the invariant mass (i.e. the "rest mass") does not change over time, but rather that the invariant mass (i.e. the "rest mass") does not depend on the frame of reference. HOOTmag (talk) 20:19, 18 May 2013 (UTC)

Irrespective of any particle's average speed, for closed systems, energy conservation requires that c = sqrt(E/m) be constant (AKA mass-energy equivalence). --Modocc (talk) 21:16, 18 May 2013 (UTC)

As for the principle of "energy conservation": it means that for closed systems, E=mc² is constant: This does not mean that for closed systems c is constant - but rather that for closed systems mc² is constant, while m and c may vary. As for the principle of "mass-energy equivalence": If c changes over time, then this principle just means that - the mass existent at any given moment - is equivalent to the energy existent at that very moment, but still this principle does not let you conclude that - the mass existent at any given moment - is equal to the mass at the following moment. HOOTmag (talk) 22:34, 18 May 2013 (UTC)

Mass-energy equivalence and, more generally, its mass-energy conservation are well-established. A changing mass results in an exact corresponding change in energy. With conservation, should c and m change but not E then you don't have an equivalence relation.--Modocc (talk) 22:46, 18 May 2013 (UTC)

First of all, in order to prove the equation E_k=(m-m₀)c² - one does not need to assume that c does not change over time - but rather to only assume that c does not depend on the frame of reference; Whereas the simpler equation E=mc² is only an (unprovable) generalization of the (provable) equation E_k=(m-m₀)c². As for the very principle of Mass-energy equivalence: It is one possible interpretation - among some others - for the (unprovable) generalized equation: E=mc². Of course, the (unprovable) generalized equation itself does not claim that E is equivalent to m, unless we assume that the invariant c - which does not depend on the frame of reference - does not change over time either. Another possible interpretation for that (unprovable) generalized equation could claim, that c - which does not depend on the frame of reference - does vary in time, thus no "equivalence principle" would arise.

Second, even if we accept the "equivalence interpretation", it may help us in closed systems only. How about open ones - in which c may (apparently) change over time? HOOTmag (talk) 23:49, 18 May 2013 (UTC)

The constancy of c = sqrt(E/m) has been validated by numerous experiments that have included open systems. See the articles I linked to for more on this. --Modocc (talk) 00:14, 19 May 2013 (UTC)

I haven't claimed that c changes over time, but rather that c may change over time. I'm talking from a hypothetical point of view, and my original question is hypothetical: Which relativistic equation contradicts the hypothetical assumption that c may change over time? HOOTmag (talk) 00:23, 19 May 2013 (UTC)

Its been speculated that c has changed, could change, or is perhaps different in other parallel universes. There is nothing inherently contradictory about that kind of speculation other than the fact that its fictitious because there is no evidence for it. --Modocc (talk) 00:58, 19 May 2013 (UTC)

In other words, there is a difference between the constancy of c among the frames of reference, and the constancy of c during time: one can mathematically infer the first constancy - from some relativistic equations (as I've showed above by the equation of time dilation), whereas one can't mathematically infer the second constancy - from any relativistic equation. This means that the second constancy is an experimental fact only, yet not a substantial/essential property of the fundamentals of Relativistic Mechanics. Is this what you claim? HOOTmag (talk) 01:10, 19 May 2013 (UTC)

Its incorrect to infer invariance of c from time dilation. -Modocc (talk) 02:24, 19 May 2013 (UTC)

What do you mean by "incorrect"? I have correctly inferred - the invariance of c - from the equation of time dilation, in my response on 17 May at 16:03, as you can see above in this thread. On the other hand, if you just mean that I was not methodologically allowed to make this inference - although it's a mathematically correct inference (as I have already shown in this thread on 17 May at 16:03), then you have probably missed my original question. Please notice that what I have been asking about (along this thread), is whether Special Relativity must assume the constancy of c in spacetime - in order to develop the relativistic equations, just as Special Relativity must assume the invariance of c - in order to develop the relativistic equations, i.e. I've been asking whether there is any (well known) relativistic equation, e.g. any Lorentz transform, or any Minkowski invariant (and the like), which contradicts the assumption that c varies in spacetime. I haven't been asking that about the invariance of c, because I had already known that Special Relativity must assume the invariance of c - in order to develop the relativistic equations, i.e. I had already known that there were some relativistic equations, e.g the equation of time dilation, which contradicted the assumption that c depended on the frame of reference, as I had already proved in this thread on 17 May at 16:03. HOOTmag (talk) 06:12, 19 May 2013 (UTC)

Sorry, but substituting c(x,t) in f(c) only shows that c(x,t)=c is a solution of f(c). It doesn't prove invariance. Modocc (talk) 09:41, 19 May 2013 (UTC)

Sorry, but I have never proved anything about c(x,t), so I don't know what you're talking about. As you can see in this thread (on 17 May at 16:03), I have only proved - from a (well known) relativistic equation (of time dilation) - that every velocity v satisfies c(v)=c(0). Hence, every pair of velocities v,v' satisfies c(v)=c(0)=c(v'). Hence, c is invariant (i.e. does not depend on the frame of reference). QED. HOOTmag (talk) 10:10, 19 May 2013 (UTC)

You show that c(v)=c(dx/dt)=c are solutions of the time dilation equation. Such an invariance of c (whether it be with respect to space or time) is certainly consistent with the fact that this time dilation is true, but it does not prove what was actually assumed to begin with, that c(v) = c. Except for the substitution you made, your second equation is merely the first equation. Modocc (talk) 10:45, 19 May 2013 (UTC)

If you follow my proof, you can realize that - not only have I proved for every velocity v that the identity c(v)=c(0) is a possible solution of the equation of time dilation - but also that I have proved for every velocity v that the identity c(v)=c(0) is the only possible solution of the equation of time dilation (because the proof is based on identities, whereas every identity in the world must point at a unique solution - since "two" different things can't be equal in any identity). Hence (by substituting v' for v) , it's also provable for every velocity v' that the identity c(v')=c(0) is the only possible solution of the equation of time dilation. By combining both identities mentioned above, we infer that every pair of velocities v,v' satisfies c(v)=c(v'). Hence c does not depend on the frame of reference. QED. HOOTmag (talk) 11:21, 19 May 2013 (UTC)

The constancy of c can be obtained in a manner that doesn't depend on light speed invariance, but since my critique (which I believe to be valid) of your proof is only valid if its understood, I will desist on any further comment about it than I've written above and further down, below. Modocc (talk) 12:01, 19 May 2013 (UTC)

Why do you think your critique may not be understood? Since I've understood you up to now (although I haven't agreed with you - which is another matter), so I don't see why I won't understand you from now on. HOOTmag (talk) 12:21, 19 May 2013 (UTC)

See my reply below. --Modocc (talk) 14:33, 19 May 2013 (UTC)

Suppose $c(x,t)$ is not constant, and a boost in the $x$ direction with velocity $v$ can still be represented by a Lorentz-like form:

${\begin{aligned}t'&=\gamma \left(t-{\frac {vx}{c(x,t)^{2}}}\right)\\x'&=\gamma \left(x-vt\right)\\\gamma &={\frac {1}{\sqrt {1-{\left({v \over c(x,t)}\right)^{2}}}}}\end{aligned}}$

Consider the inverse boost applied to the new frame, which implies:

${\begin{aligned}t&=\gamma '\left(t'+{\frac {vx'}{c'(x',t')^{2}}}\right)\\x&=\gamma '\left(x'+vt'\right)\\\gamma '&={\frac {1}{\sqrt {1-{\left({v \over c'(x',t')}\right)^{2}}}}}\end{aligned}}$

Simpliying we get:

$x=\gamma '\left(\gamma \left(x-vt\right)+v\gamma \left(t-{\frac {vx}{c(x,t)^{2}}}\right)\right)$

$\Rightarrow {\gamma ' \over \gamma }=1$

$\Rightarrow c'(x',t')=c(x,t)$

The easiest way to deal with this, is simply to give up and say that $c$ was in fact a constant. However, one can adopt the alternative point of view, in which $c'(x',t')=c(x,t)$ defines how the speed of light field transforms under a change of reference frame. If you do that, then different observers will necessarily have qualitatively different perspectives on those changes. For example, there will be a privileged frame where ${\partial c \over \partial x}=0$ at the origin, implying that the change in $c$ appears locally to be purely timelike, while all other reference frame believe the change occurs over both space and time. These sorts of things play havoc with the notion that all observers are equal, which you pretty much have to throw away if you want to propose that $c$ varies in space and time. Dragons flight (talk) 01:08, 19 May 2013 (UTC)

Unfortunately, you didn't prove what was to be proven: I've asked whether it's provable that - every x,t,x',t' satisfy c(x,t)=c(x',t'), whereas you have only proved that - every x,t,x',t' satisfying the equations you have presented at the beginning of your last response - satisfy c(x,t)=c'(x',t'); In other words: you just proved, that c was not dependent on the frame of reference, as I did in this thread - more simply - on 17 May at 16:03. So, just to make things clearer, let's put aside the complex case - involving some frames of reference - you have dealt with, and let's discuss the simplest case - involving one frame of reference only. My question is (and has always been) whether you can infer, from any set of (well known) relativistic equations, that every x,t,x',t' satisfy c(x,t)=c(x',t') in that frame of reference. HOOTmag (talk) 08:14, 19 May 2013 (UTC)

Of course that can't be proved! "For all x, prove f(x) = g(x) ... assuming f ≠ g" - and if you've had any inkling of mathematics, you know how preposterous that is! It's trivial to construct a counterexample! This is called an unphysical equation, and it's a hallmark of Aristotelian physics - rather, the development of a theory from axioms without ever stopping to check whether the theory corresponds to experimental observation. In physics, we do not prove equations. We use them, and only when they are useful.

This discussion has gone on for a long time and is getting you no closer to the answer you seek. What reference material are you looking for - a book, a website, a college course guide - that will help you find what you need? Nimur (talk) 09:34, 19 May 2013 (UTC)

You ignore two facts:

1. As I have already shown in this thread (on 17 May at 16:03), it's mathematically provable - from some (well known) equations of Relativistic mechanics - that c does not depend on the frame of reference, i.e. that every pair of velocities v,v' satisfies c(v)=c(0)=c(v'). So I just wanted to know whether it's also mathematically provable - from any set of (well known) equations of Relativistic mechanics - that c does not depend on time either, i.e. that every pair of moments t,t' satisfies c(t)=c(0)=c(t').

2. All of experimental information we have accumulated - really approves of the assumption that c does not depend on time, i.e. that every pair of moments t,t' satisfies c(t)=c(t'). So I just wanted to know whether this experimental fact can also be mathematically inferred from any set of (well known) equations of Relativistic mechanics, just as we can mathematically infer a parallel conclusion about the invariance of c with respect to frames of reference. HOOTmag (talk) 09:55, 19 May 2013 (UTC)

With relativity, invariance of c (or the Lorentz transformations) is usually assumed with respect to both space and time. As I've said above, you show that this invariance/constancy is consistent with the formula which already denote c to be a constant and from what I can discern, this consistency is your only result. Its generally known that relativity begins with its postulated invariance(s) to arrive at models contrary to any simpler model that would assume prerelativistic velocity addition, because measurements of light waves show that the non-relativistic Doppler has an apparent extraneous second-order term and therefore published non-relativistic models have not ever accurately modeled the matter-waves' wavelengths, frequencies and energy (and that sorry track record doesn't mean we cannot ever do so). Gravitational theories involving light speed force carriers that at one-time competed with relativity also didn't get the energies involved correct either (for basically the same reason) and therefore were lacking. The thing about paradigms though, such as relativity, is that one can show sets of statements are consistent with other statements, but that doesn't actually prove that the paradigm's statements (some of which are assumed and/or are held to be "fact" based) are correct, which is why Occam's razor and various evidence is important. -Modocc (talk) 11:43, 19 May 2013 (UTC)

Yes, I know that "invariance of c (or the Lorentz transformations) is usually assumed with respect to both space and time". However I have been asking whether it's necessary to assume this for developing all of the (well known) equations of Relativistic mechanics.

No, I have shown - not only consistence - but necessity as well, i.e. I have proved that the identity c(v)=c(0) is the only solution of the equation of time dilation. You can realize that by just following my strict proof, but if you don't want to review it, then let me test you: Can you give me another solution of the equation of time dilation? If c(v) is not equal to c(0), then it's equal to what? Give another value, other than c(0) (e.g. c(0)+1 and likewise), and I will show you that such a value contradicts the equation of time dilation! HOOTmag (talk) 12:14, 19 May 2013 (UTC)

As I mentioned up the page, the time dilation formula you used was derived under the assumption that c is invariant with respect to space, time, and frame. It's not really a proof if you start your analysis by assuming that your conclusion is true. I already gave you a modified version of the time dilation formula that you would need to use if you actually want to consider the case that $c_{v}\neq c_{0}$. Dragons flight (talk) 19:44, 19 May 2013 (UTC)

As I have responded up the page, I hadn't assumed that $c_{0}=c_{v}$. You thought I had, because you thought I had used the same diagram you used, and also because you thought I had used the Pythagorean theorem for calculating the length of path - as you used, whereas I really used the Pythagorean theorem for calculating the length of velocity. To sum up, my calculation is correct and assumes nothing in advance. For more details, see my direct response to your detailed response up the page. Anyways, my original question was not about whether one can prove the invariance of c (i.e. with respect to frames of reference), but rather about whether one can prove the constancy of c (i.e. with respect to time and space). HOOTmag (talk) 21:36, 19 May 2013 (UTC)

This is not really a proper venue, but its sufficient to say that an apparent (non-relativistic) invariance c = c'(v) can be a result of conflating distinct, reference frame dependent, derivations for c: {c, c', c' ',...} with an appropriate model which involves velocity addition. In other words, each observer computes c even though the underling physics is not relativistic. -Modocc (talk) 14:33, 19 May 2013 (UTC)

You claim that there are also some kinds of non-relativistics mechanics which result in the invariance c = c'(v); As I understand, you claim this new claim - not in order to reject my claim that the invariance c = c'(v) is the only possibility for c under Relativistic mechanics (because your new claim does not contradict my claim about the invariance of c) - but rather in order to claim that Relativistic mechanics must assume the constancy of c in spacetime because invariance alone is consistent with some kinds of non-relativistic mechanics as well. So, let me remind you, that Einstein did infer his Relativistic mechanics (e.g. Lorentz transforms and the like) - from the invariance c = c'(v) alone, so I suspect your new claim is against Einstein's opinion. To make things clearer, would you like to give any new equation of the "non-relativistic mechanics" you propose, so that the new equation may contradict any of the (well known) relativistic equations? HOOTmag (talk) 18:33, 19 May 2013 (UTC)

Yikes, to be clear, there are two claims to address: 1)that a different value for c contradicts time dilation (I agree with this assertion) and 2)a different value for c contradicts light speed invariance and time dilation. Both of these claims do not necessarily get contradicted because the mere correlation of these two different claims does not imply that they must logically follow from each other. With Einstein's work, light speed invariance implies time dilation, however, time dilation does not imply light speed invariance if we expand this discourse to non-relativistic assumptions since with a non-relativistic model a value different from c should not get inserted into the time dilation equation (and to do so would contradict it), yet in this context, its an apparent invariant c that gets derived and not an actual invariant c. The reason is simple: it matters whether different observers actually arrive at their measurement for c using identical yardsticks or not. If observers' data vary very slightly with humidity (acceleration in our case), we generally infer that the yardsticks are not identical and have changed in some subtle way, such as by expanding or contracting. However, according to relativity, proper yardsticks (proper time and proper distance) are identical, and with the alternative model, the proper yardsticks used for different inertial frames are not identical in general. Showing, within the proper venue of course, why yardsticks are not always identical and how my derivations entail time dilation and other relations involving the Lorentz factor turns out to be only somewhat difficult (obviously its not a cakewalk) and enlightening (for me at least). Modocc (talk) 20:08, 19 May 2013 (UTC)

• You claim: "With Einstein's work, light speed invariance implies time dilation". I think your current claim contradicts your response (of 19 May at 14:33) preceding your last response, unless I misinterpret you in the expression "time dilation". When I say "time dilation" I just mean the relativistic equation of time dilation: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c^{2}}}}$ , and if $c$ had depended on the inertial frame - then that equation would have meant: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ .
• You claim: "time dilation does not imply light speed invariance if we expand this discourse to non-relativistic assumptions". When I say "time dilation" I just mean the relativistic equation of time dilation: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c^{2}}}}$ , and if $c$ had depended on the inertial frame - then that equation would have meant: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ . Please notice that I have already proved (on 17 May at 16:03) that this relativistic equation of time dilation necessarily implies the invariance of c (i.e. with respect to frames of reference), as opposed to your current claim.
• You claim: "with a non-relativistic model a value different from c should not get inserted into the time dilation equation". of course! The time dilation equation must be of the form $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c^{2}}}}$ , yet if $c$ had depended on the inertial frame - then that equation would have meant: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ . However, you had claimed that the identity c(v)=c(0) is not a necessary solution for the equation of time dilation, so I requested to give me another solution, that's all. If you think it's impossible to give another solution, then this proves that the identity c(v)=c(0) is the only solution for the equation of time dilation - just as I have always claimed.
• As for the difference between the relativistic model and the non-relativistic models satisfying the invariance of c, you claim that "according to relativity, proper yardsticks (proper time and proper distance) are identical, and with the alternative [non-relativistic] model, the proper yardsticks used for different inertial frames are not identical in general". I'm asking you again: Would you like to give here any new equation of the "non-relativistic models", so that the new equation may contradict any of the (well known) relativistic equations? HOOTmag (talk) 22:37, 19 May 2013 (UTC)

As pointed out above $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ is simply NOT the correct form of the time-dilation equation for an assumption of frame dependence. You need to reexamine the derivation of the time dilation equation if you want to accurately consider the consequences of allowing a frame-dependent speed of light. In that case the correct form of the time dilation equation becomes $\Delta t_{v}={\frac {c_{0}}{c_{v}}}{\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$. Dragons flight (talk) 22:51, 19 May 2013 (UTC)

I think you confuse the relativistic "time-dilation equation" (after adapting it to an assumption of frame dependence) with a purely mathematical equation which does not assume any relativistic assumption (nor Lorentz transformation). As for the so-called "time dilation equation" (i.e. the relativistic one), it must be of the form $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c^{2}}}}$ , whereas adapting it to an assumption of frame dependence - by simply substituting c_v for c - makes it: $\Delta t_{v}={\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$ . On the other hand, as for the purely mathematical equation which does not assume any relativistic assumption (nor Lorentz transformation): It's simply $\Delta t_{v}={\frac {c_{0}\Delta t_{0}}{\sqrt {c_{v}^{2}-v^{2}}}}$ , which is mathematically equivalent to a more complex equation: $\Delta t_{v}={\frac {c_{0}}{c_{v}}}{\frac {\Delta t_{0}}{\sqrt {1-v^{2}/c_{v}^{2}}}}$. For more details, see my direct response to your detailed response in which you presented this complex form for the first time. Btw, I used (on 17 May at 16:03) the combination - of the purely mathematical equation - with the relativistic "time-dilation equation" (after adapting it to an assumption of frame dependence), in order to infer the invariance of c (i.e with respect to reference frames), whereas my original question has been whether one can similarly infer also the constancy of c (i.e with respect to spacetime). HOOTmag (talk) 00:05, 20 May 2013 (UTC)

Steroids and bodybuilding

Is it possible to get bodies like these [1][2] without steroids? --Yoglti (talk) 06:41, 22 May 2013 (UTC)

Oh yes, it takes a little skill, but you can use this. 86.4.181.3 (talk) 07:00, 22 May 2013 (UTC)

Biology

Give the biological significance of Van der Waal's forces? — Preceding unsigned comment added by Titunsam (talk • contribs) 11:03, 22 May 2013 (UTC)

I'll say it is a kind of weak force, similar to that that tie students to their homeworks, it's a weak link. OsmanRF34 (talk) 12:31, 22 May 2013 (UTC)

Have you tried reading Van der Waals force (and gecko)?--Shantavira|^{feed me} 13:12, 22 May 2013 (UTC)

Name the following psychiatric symptoms

What are the psychological terms for the following symptoms:

1. Destroying objects that reminds an unpleasant past incident 2. Performing mental ritual such as touching the door repeatedly before leaving home believing it will be lucky --Yoglti (talk) 11:14, 22 May 2013 (UTC)

1. Displacement (psychology)?

2. OCD? OsmanRF34 (talk) 12:24, 22 May 2013 (UTC)

3. Ignoring the 'no medical advice' rule? AlexTiefling (talk) 11:14, 22 May 2013 (UTC)

3 . Selective perception? OsmanRF34 (talk) 12:25, 22 May 2013 (UTC)

This question is either a request for medical advice, to whit a diagnosis of the possible symptoms he described, or a homework question. Either way it's not something we should answer, unless the OP shows us what effort he has made to find the answer himself, and where he got stuck. Wickwack 120.145.48.50 (talk) 13:00, 22 May 2013 (UTC)

Butterfly effect and scientific method

How can someone test scientifically the existence of a butterfly effect in weather prediction or other complex dynamic systems? I understand that it's not about an unknown butterfly somewhere causing havoc by simply flapping its wings, but about how minimal alteration of the starting system can alter completely a whole system. It's clear that if it were a die, you just could change something really small and see what happens, reaching the conclusion that a butterfly effect exits in tossing dice. But, where is the hypothesis-experiment-conclusion when it comes down to bigger stuff like the weather? OsmanRF34 (talk) 13:03, 22 May 2013 (UTC)

Half the problem is that the butterfly effect is a plain-english description of a phenomenon in chaos theory; and therefore, it is a mathematical development, and not a scientific fact. So, it's not subject to "hypothesis-experiment-conclusion" cycle any more than "2+2" is. It is a mathematical result that certain functions have immensely variable results; applied mathematicians can be very precise and specific in describing these characteristics. For example, the Lyapunov exponent is one quantitative measure of stability. In Control theory, we use phase margin and frequency response as a measure of system instability.

So this is more a matter of whether a mathematical model is applicable to a physical phenomenon. When physicists or engineers study air flow in experimental conditions, they deduce mathematical equations that appropriately model the observations. We can therefore apply the stability measurements to those models, allowing us to understand the limitations of the model's predictive power. This is sometimes formalized as sensitivity analysis. More theoretical physicists use the phrase "the calculus of variations" to refer to the same style of analysis when performed without an electronic calculator.

No reasonable scientist attempts an actual controlled experiment gauging behavior differences with- and without- the controlled release of a butterfly. Nimur (talk) 13:36, 22 May 2013 (UTC)

All Nimur's points are spot-on, but I'll add that there are some "experiments" that people perform to detect if a real system is chaotic (or perhaps more pedantically, is well-described by a model that has chaotic properties). So, if we measure a system, and show evidence that its dynamics are chaotic (with a positive Lyapunov exponent), then in a sense you could say that someone has demonstrated the butterfly effect in a real system. For a feel for how this works, google /detecting chaos in time series/, like so [3]. For another real-world "test of the butterfly effect" (please, understand this is loose phrasing), you might be interested in industrial application of chaotic mixing. The mixing properties of some chaotic systems are basically the same as "the butterfly effect", in that they both are results of the divergence of initially nearby states, due to a positive Lyapunov exponent. See e.g. this professor's web-bio [4], which has a nice overview of applications of chaotic mixing. The mixing is only effective in the real world because the math that describes it also displays the butterfly effect. Finally, the Baker's map is a chaotic process that you can test at home -- start with two similar arrangements of dough, iterate the map on each slab n times, see how differently they turn out! SemanticMantis (talk) 15:22, 22 May 2013 (UTC)

The above answers are quite good. I would also add, that one definitely does run experiments on global climate models in order to understand the effect of chaos, specifically, the role of sensitive dependence on initial conditions in influencing simulation results. It is now often routine to repeat computer model experiments subject to small perturbations in initial conditions in order to see how the results evolve differently. This allows one to differentiate which parts of the behavior may be predictable from the parts that are heavily impacted by chaos and may only be described in a broadly statistical sense using probabilities. Of course, one needs to make a small leap of faith that the computer models are an accurate representation of our planet's weather / climate, but it is certainly true that the computer models demonstrate the butterfly effect. Dragons flight (talk) 15:44, 22 May 2013 (UTC)

Again, the answers above are good. I take issue though with Nimur's statement "So this is more a matter of whether a mathematical model is applicable to a physical phenomenon." because it may give the false impression that the butterfly effect is due to some limitation of the models. That's not the correct interpretation of the effect. The models do display the butterfly effect not because they aren't good models. They display the effect because they ARE GOOD models and (correctly) capture a feature of real weather systems - namely, the butterfly effect. Dauto (talk) 17:17, 22 May 2013 (UTC)

It's useful to explain how this came about. In the early 1960's Edward Lorenz was working on computer simulations of weather systems tracking across the North Atlantic over a simulated 2 week period. His simulations produced convincing results and he was happy. One day he had to re-run a previous simulation. One particular parameter of the simulation should have been set to 0.506127 - and had been set to that on that first run. But on the second run, he only bothered to type 0.506...meh, close enough, right? Wrong! That tiny change of one or two parts in ten thousand was enough to produce UTTERLY different results. That's what "chaos theory" is all about. It's perhaps better called "sensitivity to initial conditions". If a teeny-tiny change at the start of some process is magnified to a GIGANTIC change in the end result, then the process is said to be "chaotic". If one part in 10,000 can change the weather over a couple of weeks of simulated time - then one part in 100,000,000 will create the same amount of change over a month, one part in 10,000,000,000,000,000 over two months. Over six months, the displacement of a single atom over the diameter of an atom is enough to cause drastic changes in the way the atmosphere ends up. Hence, the flapping of a butterfly's wing is more than enough to cause violent weather anywhere on the planet - given enough time...or to cause violent weather not to happen...or to have no effect whatever. Either way! SteveBaker (talk) 18:58, 22 May 2013 (UTC)

It may also be worth mentioning here that continuing along Steve's line of reasoning, not even very far past the "single atom over the diameter of an atom", quickly gets you down below quantum uncertainty. The butterfly effect tends to be presented as an example of "deterministic chaos", but by my lights the "deterministic" part of that formula is undemonstrated (and has the burden of proof). The default view should be that the exact weather in a specific location, say, two years from now, is simply not determined by the current state of the world. --Trovatore (talk) 21:26, 22 May 2013 (UTC)

But, why do you get stable overall patterns, given that a "butterfly" can bring the whole system out of sync? Some places are mostly rainy, and some are mostly sunny. OsmanRF34 (talk) 19:05, 22 May 2013 (UTC)

Congratulations, you've spotted a flaw in overly-simplified analogies for very complicated (and complex) subjects :) My answer here is from the math perspective, I'm not going to make any deep statements about the weather. Keep in mind that the state space of the atmosphere is basically infinite dimensional, and the kinds of models applied often operate in Hilbert spaces, or Banach spaces, or other more exotic locales. So there's plenty of "room" for different types of behavior in the same system. Point is, just because some dimensions have chaotic dynamics, doesn't mean they all do. Here's an example of a simple system that has both chaotic and fairly predictable dynamics. Take a large, heavy pendulum, say a car hanging from a crane. Next, put a small gizmo like one of these chaotic pendulums [5], [6] inside the car, and send the whole thing swinging. Because of the separation of mass scales, the little whirly bit hardly affects the car, and we can predict the gross motion of the car pretty well. But that little spinner remains totally chaotic, and we can't predict it's motion at all...

So -- of course there is some predictability to weather, and some stable structures, but there is also deterministic chaos. The jet stream is a good example of both. No butterfly will ever destroy the jest stream, but its precise path is very difficult to predict. SemanticMantis (talk) 20:00, 22 May 2013 (UTC)

The reason those long term patterns persist is that this extreme sensitivity is to initial conditions. The flapping of that butterfly six months ago has a drastic effect on the weather patterns of the entire planet - but the flapping of a butterfly 30 seconds ago has no noticable impact on today's weather. The factors that make it warmer in some places than others are continual inputs - such as the sun being higher in the sky near to the equator - or the persistent existence of some large body of water producing humidity. Those effects continually nudge the system back towards predictability. It is the balance between the chaotic behavior and the nudging back towards stability that compete to generate the weather that we see - which is broadly predictable over multiple year averages, wildly unpredictable over spans of four of five days out to weeks, then predictable again for spans of a day or two. These stabilizing effects keep the averages straight - and the fact that chaotic behavior is only able to magnify short-term events over long periods of time keeps the weather predictable over the shorter timescales. SteveBaker (talk) 16:46, 23 May 2013 (UTC)

On "deterministic" — see my remarks above, after Steve Baker's contribution. --Trovatore (talk) 21:26, 22 May 2013 (UTC)

Point taken. I did say I was focusing on the math side of things, where the chaos is demonstrably deterministic. Whether non-deterministic or quantum effects have a non-negligible influence on real weather, I cannot say :) SemanticMantis (talk) 22:00, 22 May 2013 (UTC)

Dauto above is confused about what a model is and what we know about the real world. What we know, or think we know about the world, is just the model. Nimur is right when he questions whether the model fits the data or not. It might be the more valid one right one, but might be substituted in the future by something better. That's science. No one suggested that the butterfly effect was a flaw of weather models. Knowing it, is knowing a detail about the most valid model that we have. 83.41.31.29 (talk) 20:04, 22 May 2013 (UTC)

Damp proof course

Is a damp proof course part of the building code in the usa for a concrete block house? --Jason1267 (talk) 13:53, 22 May 2013 (UTC)

In the United States, building codes are set at the state, county, and municipal levels. You'd need to be more specific about location. Nimur (talk) 13:58, 22 May 2013 (UTC)

I am interested in Columbus, Ohio and Miami, Florida--Jason1267 (talk) 14:02, 22 May 2013 (UTC)

For example, Columbus' Department of Building and Zoning links to the 2011 Ohio Building Code. You can telephone their office for guidance. Often, the city will refer you to a building contractor to answer these sorts of questions, because the answers almost always depend on lots of details; but you can survey the code yourself to get an idea. Nimur (talk) 14:08, 22 May 2013 (UTC)

Which is bigger?

Which is the bigger ratio, one atom vs one human being, or one human being vs the entire galaxy?114.75.53.116 (talk) 16:10, 22 May 2013 (UTC)

Ratio of what? Size? Mass? Volume? uhhlive (talk) 16:12, 22 May 2013 (UTC)

Do you mean by length, by mass, or something else? You can get a rough answer from Orders_of_magnitude_(length) or Orders_of_magnitude_(mass) by calculating the ratios directly. SemanticMantis (talk) 16:15, 22 May 2013 (UTC)

As pointed out above, the question could've been more precise. Turns out that Galaxy-to-human ratio is much larger than the human-to-atom ratio no matter the criteria used. Dauto (talk) 17:42, 22 May 2013 (UTC)

One vivid analogy I have found useful to remember for comparison is that if a raindrop were the size of the earth, each of its water molecules would be the size of a basketball. μηδείς (talk) 02:59, 23 May 2013 (UTC)

Buying pure elements

Where can I easily get:

List of pure and metallic elements
The following discussion has been closed. Please do not modify it.
metallic lithium metallic sodium metallic potassium metallic rubidium metallic caesium metallic beryllium metallic calcium metallic strontium metallic barium metallic radium metallic uranium metallic plutonium metallic tantalum metallic cadmium metallic gallium metallic indium metallic thallium metallic scandium metallic yttrium pure polonium pure fluorine pure chlorine pure bromine pure iodine pure astatine pure boron pure arsenic pure argon pure neon pure krypton pure xenon pure radon?

Whoop whoop pull up ^{Bitching Betty | Averted crashes} 16:59, 22 May 2013 (UTC)

Fisher Scientific and McMaster-Carr. A few of these (Polonium?) cannot be easily gotten anywhere. Nimur (talk) 17:01, 22 May 2013 (UTC)

Polonium can be bought at United Nuclear. In the same way as many other radioactive isotopes. OsmanRF34 (talk) 17:55, 22 May 2013 (UTC)

Polonium is a component in atom bomb neutron generators, and for this reason is a restricted substance. 24.23.196.85 (talk) 02:38, 23 May 2013 (UTC)

What is your geographical location? Most of these things can be obtained in pure analytical form, from local laboratory suppliers. However, since the Home Guard (or whatever they are called where you are) are looking for anybody that can possibly be sourcing materials for terrorist devices, expect a visit from the men in black or the FBI. P.S. Why, Oh Why, are you asking? Why do you need this stuff?Aspro (talk) 17:16, 22 May 2013 (UTC)

To be fair, Fisher sells these under their "Science Education" program, typically marketing to high school and college-level chemistry students and teachers. Items that are more hazardous - like polonium and radon - are not usually available without raising a few hackles; but with lots of paperwork, and a reasonable degree of oversight and accountability, a credible educational institution can often acquire these sorts of things; they do have uses other than causing havoc. But just because you're an enthusiast with no ill intention, that doesn't mean you won't get a little extra attention at the airport for the rest of your life! Nimur (talk) 17:21, 22 May 2013 (UTC)

Tiny amounts of polonium are available in such things as anti-static brushes, with no special red tape needed. --Trovatore (talk) 18:54, 22 May 2013 (UTC)

You can get an entire element collection here, from the Red Green & Blue Company, for around 500 pounds. There are also occasional element collections on eBay, usually in the range of a few hundred dollars. --Bowlhover (talk) 18:48, 22 May 2013 (UTC)

Not really credible — how do you sell a sample of francium? My guess is that the "francium" tube contains a sample of natural uranium ore, which at any given time will contain a few atoms of francium. Probably the same for several of the other short-lived elements in the U-238 decay chain. --Trovatore (talk) 18:52, 22 May 2013 (UTC)

The company doesn't claim to have a pure sample of every element. From the FAQ: "Two radioactive elements (thorium and uranium) are provided as small metal samples. Two others, radium and promethium, are presented in the form of small dabs of luminous paint [...] The remaining seven radioactives are represented by small uranium or thorium bearing ores. These naturally occurring specimens contain complex decay chains of radioactive elements and at any given time will harbour a small quantity of the specified element." --Bowlhover (talk) 09:22, 23 May 2013 (UTC)

Nothing in ebay seems genuine anymore. Anyway, a serious company could ship radioactive material that have a short half-life. It only would need to ship it shortly after obtaining it, and not keep it on stock. OsmanRF34 (talk) 19:01, 22 May 2013 (UTC)

Well, the longest-lived isotope of francium has a half-life of 22 minutes, which means that if the shipping company could somehow ship a gram of it in 24 hours, by the time you got it, by my calculations, there would be about 50 atoms left. Of course the heat and radiation it evolved in the mean time would — probably not have gone unnoticed. --Trovatore (talk) 20:27, 22 May 2013 (UTC)

According to Theodore Gray (maker of the periodic table table), the RGB set's sample of francium consists of a chunk of uranium ore, which contains a small but constant amount of francium. --Carnildo (talk) 23:31, 22 May 2013 (UTC)

Well, that was almost exactly my guess, if you look at my comment of 18:52 22 May 2013 above. Of course I can't rule out the possibility that I heard this somewhere before. --Trovatore (talk) 00:39, 23 May 2013 (UTC)

There have been a few suppliers that sell small "samples" and complete sets as diplays of one sample of each of the elements in the periodic table. Theodore Gray and his associates have determined that for radioactive elements that are dangerous and/or have short half lives, or just cost too much, what is supplied is often just an inert material that is supposed to look like the real element (and often does not even do that. the visual appearance of some of the rare high weight elements is not known for sure anyway). See http://periodictable.com (Element Collection, Inc) - highly recomended. Soem elements are not chemically stable and/or are dangerous to handle. In these case, what is typically supplied is some stable well known compound or well known use. Wickwack 121.215.149.172 (talk) 23:52, 22 May 2013 (UTC)

Using small LCDs for other purposes

The very small and simple LCD screens we find in cheap watches, which display only black numbers (each made by four vertical and three horizontal sticks), are just grey coated glass slides. Theoretically I know they have "liquid crystals" in them which turn black from transparent when current is applied. I don't find any visible inlets which could take electricity inside them. Yes they do have soft a rubber line on their base which contacts the numerous metal contacts held in a long line along the circuit board that clearly seems to be the appropriate number of "sticks" that form the digits. My problem is that how can one directly manipulate them ? Is the usual 1.5 direct current from a small battery appropriate ? 124.253.173.16 (talk) 19:24, 22 May 2013 (UTC)

Unfortunately LCD if far more complicated to drive then LEDs. They are typically driven by a special driver circuit because they require AC, not DC. I have some experience with amateur electronics and honestly, I wouldn't bother attempting it. If you want to play around with Seven-segment_displays, I would storngly recommend you just buy a couple of LED units instead, something like this, dirt cheap and far easier (and prettier IMHO). Then you can play around with actually displaying stuff, not strain your brain working out how to display stuf in the 1st place. Vespine (talk) 23:08, 22 May 2013 (UTC)

I have no direct experince of watch displays, but I have designed circuits using the larger LCD displays used in small travel clocks, pocket digital multimeters, and the like, and I would asume that they are very similar. In all these displays, conventional connectors are not used. Instead, conductive traces embedded in elastomeric plastic is used, as the glass should be protected against mechanical stress and vibration, and the current flow is minute, so very high resistance does not matter. Typically, about 3 volts is required to turn a segment on (make it black). A micropower transistor invertor is used to get a stable 3V or so from a single button cell (1.2 volt). To use an LCD display, you will need to identify the connection to the backplane ( a transparent sheet electrode common to all segments, as well as the connection to each segment (ie what you refered to as "sticks"). It is absolutely critical that NO DC voltage appears between the backplane and any segment connection (and betwen segments). The display will fail rapidly if even the slightest DC is present. This is achieved by starting with an accurate squarewave - by accurate I mean that it has EXACTLY unity ratio between "high" and "low" durations, as well as a clean square waveform. This squarewave is used to drive the backplane. To turn a segment off (ie transparent & showing the grey background) you apply the same squarewave to the segment connection. To turn a segment on (ie black), you apply an inverted squarewave to the segment connection - again an ACCURATE square wave, precisely timed to the backplane squarewave. It is more than possible that a tiny watch display needs less than 3V. You could discover the voltage required by constructing a circuit that can generate a two-phase square wave of variable voltage and, starting from zero, gradually increase the voltage until the segments turn black. DO NOT test with DC. Do not use more than about 30% more than what is requied to get black segments.

Ideally, you need an ocilloscope to verify you get all this right, but by using well known circuits you could get by without it. If all this does not deter you (and Vespine gave you good advice to leave it alone), I suggest you search though past issues of the magazine Elektor, which should be available at better public and university libraries, or do some good google searches - someone's bound to done it before. Keit 120.145.156.222 (talk) 23:38, 22 May 2013 (UTC)

"Non-Newtonian Play-Doh"

For a business assignment, we are to make Play-Doh (salt dough), create a brand for it, market it, etc. To be creative, I thought back to my days of elementary school when we would mix cornstarch and water to make "oobleck," and I was considering adding the oobleck substance into the play-doh mixture, which we will need to make ourselves (using 1 cup of water, 1/2 cup salt, 1 cup flour, 1 tbsp oil, 1 tbsp cream of tartar). If we added cornstarch and water to the mixture, would it make the play-doh non-Newtonian in any way? Would it ruin the mixture? Would it just not do anything? Thanks so much! 174.93.65.84 (talk) 19:52, 22 May 2013 (UTC)

Well, you could easily try it, since that whole assortment of ingredients can be bought for less than a dollar -- but I'm pretty sure you would just get a bunch of sticky glop. Looie496 (talk) 20:59, 22 May 2013 (UTC)

Mostly, I would say that oobleck is "non-Newtonian Play-Doh". That is, if you're going to get that sort of interesting sometimes-solid-sometimes-liquid response, you need to be ready to brand and market something that will spill like water (or, at best, syrup) if you tip the can over. Sure, you can make slightly-thin Play-Doh (or really thick oobleck, depending on one's perspective), but if it's thick enough to be a non-spillable kids toy, then it's too thick to do "interesting" non-Newtonian things (where "interesting" is defined as "more like oobleck, less like Silly Putty"). — Lomn 21:22, 22 May 2013 (UTC)

There certainly is Play-Doh-like material that is highly non-Newtonian (it can flow off a table, it can bounce like a rubber ball, and it splinters if hit by a hammer). We used in in chemistry lab 30 years ago, and I recently saw it in a materials lab as a demo piece. I don't think it was quite the same, but Silly Putty might help. --Stephan Schulz (talk) 21:26, 22 May 2013 (UTC)

I kinda worry that making something other than play-doh (even if it's "better" than play-doh) rather defeats the object of this marketing exercise - which is to take some relatively mundane product that everyone knows - and to make it seem exciting and interesting to your target market despite it being "just play-doh". Changing the product might invalidate the entire assignment.

You might also want to check out Flubber (material) - it's still fairly easy to make - but it has quite different properties. But it's generally considered not-kid-friendly because some of the ingredients are not things kids should be ingesting!

Also, oobleck and play-doh fill different niches. Play-doh can be used to make models - they sell machines that extrude it into interesting shapes - molds so you can make recognizable things with it - plastic parts you can stick into it - toy kitchens where small children can pretend to make meals with it. The unfortunate defining feature of oobleck is that the moment you stop exerting forces on it, it liquifies - so it's quite utterly impossible to make interesting things with it that persist for more than a few seconds. That DRASTICALLY changes the ways in which you can market it - which probably explains why PlayDoh has been around for nearly 60 years and is still incredibly popular...and oobleck and similar substances appear under various brand names and are never much more than a passing fad.

SteveBaker (talk) 16:28, 23 May 2013 (UTC)

There are a few common add-ins to that recipe that I know of. Food coloring can be used to make it any color. Things like vanilla, cinnamon, or Kool-Aid mix can be used to give it different scents. (Kool-Aid can also change the color.) They'll keep the original clay-like properties, while adding a unique twist. 38.111.64.107 (talk) 19:28, 23 May 2013 (UTC)

ADSL filter with 2xBS 6312 sockets and one ADSL (RJ11 is it?) socket...

Does such a thing exist? If so, what's it called? Cheers. --Kurt Shaped Box (talk) 22:04, 22 May 2013 (UTC)

They exist, Maplins sell them with built in surge protection as well for £15. And a quick Amazon search shows a few more (just on a basic search for ADSL filter). You won't find many though as it's easier (and cheaper) to just plug a BS6312 splitter into the filter phone socket. Nanonic (talk) 22:16, 22 May 2013 (UTC)

Thanks. Yah, I was thinking of that too, but I was having trouble finding a BS6312 splitter that had a length of cable coming from the back - as opposed to just being a box with a plug coming straight out (which would block the RJ11 socket on my existing BB filter). Then I saw one, just after posting my Q. :) --Kurt Shaped Box (talk) 22:29, 22 May 2013 (UTC)